As world attention has recently been focused elsewhere, longstanding tensions between two critical U.S. allies, Japan and South Korea, have quietly been easing. This is the result of initiatives by the leaders of both countries, as well as the concerted efforts of diplomats. That’s good news for Washington, since together the three nations can better address common security challenges and achieve shared diplomatic and economic objectives.

It may be a surprise that two democracies with the common values of freedom, free-market principles, and respect for law and human rights could be at such odds. But contentious, unresolved and highly emotional issues arising from Japan’s occupation of the Korean Peninsula from 1910 to 1945 continue to plague the two nations.

Japanese Prime Minister Shinzo Abe’s highly successful U.S. visit earlier this year appears to have triggered a policy review by South Korea’s President Park Geun-hye. With Tokyo planning to take a more active role in regional security missions, Seoul felt it was becoming increasingly isolated as it faced growing threats from China and a nuclear North Korea.

The result has been a new effort by both Seoul and Tokyo to compartmentalize difficult historic differences—continuing to seek resolutions as they work together to overcome common challenges. The South Korean and Japanese foreign, finance and defense ministers have all met recently with their counterparts. There have also been discussions to resume and augment bilateral military cooperation.

We recently witnessed this new spirit of amity at the Heritage Foundation during a rare joint appearance by Ambassadors Kenichiro Sasae of Japan and Ahn Ho-young of South Korea, as well as U.S. Deputy Assistant Secretary of State Sung Kim. The three diplomats emphasized the importance of trilateral cooperation, for example, in responding to the North Korean security threat.

But while the message from the ambassadors was encouraging, pitfalls remain on the path ahead. Real progress is on hold pending Mr. Abe’s Aug. 15 statement commemorating the 70th anniversary of the end of World War II. Few remarks have ever been awaited with so much anticipation and trepidation.

Mr. Abe’s speech will be scoured for signals of contrition and responsibility over Japan’s wartime actions. Tokyo may feel it has apologized enough and settled all matters of restitution through the 1965 treaty normalizing relations with South Korea. Yet South Korean sensitivities remain. There are suspicions, for instance, about Mr. Abe’s ambitions for Japan’s expanded military role in the region.

With the statement, the Japanese leader has the opportunity to repair strained relations with Seoul and begin a new chapter of reconciliation and cooperation. But this will require a painful acknowledgment of the past, notably by including important phrases from previous statements recognizing Japan’s responsibility, and perhaps being even more conciliatory than Mr. Abe’s predecessors.

South Korea must also be willing to move forward. It could begin by accepting the positive steps Japan has taken. Both nations’ leaders will need to show strong and bold leadership by standing up to the fervent nationalist elements in their countries that have worked against rapprochement.

The U.S. also has a role to play, since it is inexorably linked to Asia not only by history but by the need to stand firmly with its friends even when they disagree with each other. Washington should continue to play an important role as behind-the-scenes facilitator by encouraging, cajoling and even occasionally criticizing both nations in private.

Strains between Seoul and Tokyo have hindered an effective response to North Korea’s growing security threat as well as impacted important South Korean-Japanese trade ties. Warming bilateral relations could even enable coordinated policies on regional matters such as ensuring open sea lanes of communication.

The past is important, but so is the present and the future. The prosperity of Asia requires the bonds of strong and true friends, economic partners and allies. There are no better examples of these than Japan and South Korea. Their ambassadors in Washington understand this. We only hope that their capitals share the sentiment.

-Mr. DeMint is the president and Mr. Klingner is a senior research fellow for Northeast Asia at the Heritage Foundation.